Question

question
find the equation of the exponential function represented by the table below:

x	y
1	0.1
2	0.05
3	0.025

answer
attempt 1 out of 2
y = submit answer

Explanation:

Step1: Recall exponential form

The general form of an exponential function is $y = ab^x$, where $a$ is the initial value, $b$ is the growth/decay factor.

Step2: Find $a$ using $x=0$

When $x=0$, $y=0.2$. Substitute into the formula:
$0.2 = ab^0$
Since $b^0=1$, we get $a=0.2$.

Step3: Find $b$ using another point

Use $x=1, y=0.1$. Substitute $a=0.2$, $x=1$, $y=0.1$ into $y=ab^x$:
$0.1 = 0.2b^1$
Solve for $b$:
$b = \frac{0.1}{0.2} = 0.5$

Step4: Write the final equation

Substitute $a=0.2$ and $b=0.5$ into $y=ab^x$.

Answer:

$y = 0.2(0.5)^x$